Digital holographic interferometry with CO2lasers
and diffuse illumination applied to large
space reflector metrology
Marc P. Georges,1,* Jean-François Vandenrijt,1Cédric Thizy,1Yvan Stockman,1
Patrick Queeckers,2Frank Dubois,2and Dominic Doyle3
1Centre Spatial de Liège, Université de Liège, Avenue du Pré Aily, Angleur (Liège) B-4031, Belgium
2Microgravity Research Centre (MRC), Université Libre de Bruxelles,
CP165/62, Avenue F.D. Roosevelt 50, Brussels B-1050, Belgium
3European Space Research and Technology Centre (ESTEC), European Space Agency,
Keplerlaan 1, Noordwijk 2200 AG, The Netherlands
*Corresponding author: firstname.lastname@example.org
Received 14 August 2012; accepted 31 August 2012;
posted 25 September 2012 (Doc. ID 174310); published 1 November 2012
Digital holographic interferometry in the long-wave infrared domain has been developed by combining a
CO2laser and a microbolometer array. The long wavelength allows large deformation measurements,
which are of interest in the case of large space reflectors undergoing thermal changes when in orbit.
We review holography at such wavelengths and present some specific aspects related to this spectral
range on our measurements. For the design of our digital holographic interferometer, we studied the
possibility of illuminating specular objects by a reflective diffuser. We discuss the development of the
interferometer and the results obtained on a representative space reflector, first in the laboratory
and then during vacuum cryogenic test.© 2012 Optical Society of America
090.1995, 090.2880, 120.3940, 040.3060.
Coordinate and deformation metrology of complex
shape space structures and reflectors is a recurrent
problem addressed by space agencies and companies
worldwide. Accurate knowledge of a space structure
deformation or a reflector’s surface shape under rea-
listic operational conditions is essential to accurately
predict in orbit performance. Consequently, suitable
measurement techniques have to be developed and
validated to support relevant on-ground qualification
and verification testing. The application presented in
this paper is related to a continuous need for the
European Space Agency (ESA) to support studies
of metrology for aspheric reflectors in the infrared,
far-infrared and submillimeter ranges. Interest for
new methods was also shown in the case of strongly
asymmetric radio-frequency reflectors that depart
from a global parabolic shape through localized areas
of free-form curvature and that are used for produ-
cing asymmetric spot beams for specific ground cov-
erage telecommunications. The search for adapted
metrology techniques is made more complex because
the reflectors can be several meters in diameter. In
particular, in the project supporting our study, defor-
mation measurements were to be demonstrated on
reflectors with typical diameter of 1 m (with possible
extension of the method to 4 m), with deformations
ranging from 1 to 250 μm, with the highest possible
spatial resolution. For that purpose we have first
analyzed the potential optical noncontact methods
that were available on the market or described in
© 2013 Optical Society of America
A102 APPLIED OPTICS / Vol. 52, No. 1 / 1 January 2013
In general these can be grouped into two main ca-
tegories: (1) those using coherent light illumination,
e.g., classical interferometry  and holography/
speckle interferometry , and (2) noncoherent opti-
cal techniques based on imagery, such as photogram-
metry (or its recent digital videogrammetry version)
The second category relies on the determination of
surface coordinate points from which deformations
are obtained by subtracting two measurements. In
the case of videogrammetry, targets have to be at-
tached to or projected on the surface, while in digital
image correlation a random pattern (made of black
dots sputtered on white paint covering the object) is
necessary. In fringe projection the surface has to be
scattering enough to be able to observe the projected
two-dimensional line pattern, which is also the case
with digital image correlation using a random
projected pattern. In all cases, surfaces under test
have to be specially prepared, and this is not accepta-
ble in most space testing. Indeed the surface of flight
models cannot be equipped with targets nor covered
at too high risk for the specimen. Also vacuum ther-
mal tests generally would provoke outgassing of any
paint or retroreflector targets, which has to be
avoided, so preventing contamination. Despite this,
videogrammetry has proven recently that it was a
choice method for testing some types of space struc-
tures, making use of projected dots . However,
theresolution inposition ofpoints,andthusdeforma-
the camera, and other factors specific to the techni-
ture for videogrammetry, resolutions of 10 parts per
surements and camera positions are required, pre-
venting fast single-shot captures.
ences between the object surface and a reference sur-
face (classical interferometry) or between the object
and itself at different instants (holographic/speckle
interferometry), the resolution being driven by the
laser wavelength. In classical interferometry , sev-
eral configurations exist but generally one considers
reference wavesreflected by a high wavefront quality
element (plane or spherical) that interfere on an im-
age sensor with the object wave travelling indepen-
dently from the test object. For testing an aspheric
mirror, one has to arrange to illuminate it through
figuration. The interference between both reference
distance between two fringes is proportional to the
wavelength. When large wavefront differences are
present (which is the case with aspheres illuminated
by spherical wavefront), interferometers at visible
wavelengths quickly show a larger fringe density
than cannot be resolved for areas with large slopes.
For solving this problem, interferometers at long-
wave infrared (LWIR) range (e.g., 10.6 μm with CO2
lasers) were developed in the past under various con-
figurations like Twyman–Green  or Fizeau .
However, in the case of deep aspheric mirrors (e.g.,
parabola with very low f-number) like those found in
space telescopes, the slope variations can still gener-
ally be too high to allow use of simple spherical illu-
custom-built null lenses need to be used instead to
match the aspheric wavefront . Refractive null-lens
correctors are quite usual in the visible, but develop-
ment of such elements can become expensive in the
LWIR with the use of zinc selenide (ZnSe) or germa-
nium(Ge)materials. Despite this, wedevelopedinthe
past a high-resolution LWIR Twyman–Green interfe-
rometer  specifically for testing aspheric reflectors
of the submillimeter Planck telescope [12,13].
Holographic interferometry (HI) is also a viable
alternative used in the thermo-optical and cryogenic
performance testing of space reflectors. The advan-
tage of HI compared to classical interferometry is
that it can be applied on any kind of surface provided
that the object reflects some light toward the holo-
gram sensor. Then, instead of using an expensive
null lens, a simple spherical one that collects the
necessary rays is sufficient.
An important point for HI is the performance of the
listic conditions (e.g., under vacuum). For continuous
monitoring of large deformations, dual wavelength
ment . The use of photorefractive crystals as a
user-friendly recording medium has been intensively
investigated by Centre Spatial de Liège (CSL) group
of large reflectors [17,18], but this technique is also
very sensitive to environmental disturbances that
required development of specific phase stabilization
techniques that were complex to implement .
sented in this paper. Indeed the idea came to develop
an HI method in LWIR that will relax the stability
constraints in the setup while providing large defor-
mation displacements in a single-shot interferogram.
Given the fact that deformations to be measured on
such large reflectors are ranged between 1 and
ticular we consider digital holography (DH), which
allows instant recording and readout of holograms.
Although evidence of DH can be found during the
early years of holography , it has gained a con-
siderable interest in the past two decades due to sig-
nificant improvements of electronic imaging sensors
[21,22]. The technique allows numerical recon-
struction of diffracted orders (among which is the
image of the object of interest) through various algo-
rithms that have been developed by many groups
1 January 2013 / Vol. 52, No. 1 / APPLIED OPTICS A103
[2,23–26]. All these developments were made in visi-
ble light. Recent literature presents efforts in extend-
ing DH to other spectral ranges, from the ultraviolet
 to LWIR  and terahertz [29,30].
In Section 2 of this paper, we review holography in
the LWIR domain. In Section 3, we present some par-
ticular aspects related to the use of thermal LWIR
radiation that is of great importance to consider and
that plays no role in the visible. In Section 4, we dis-
cuss the potential setup configurations necessary to
observe large specular reflectors. We see that an in-
teresting possibility is to use diffuse illumination of
the specular object prior to numerical reconstruction
by DH. Since this was never shown in the past, we
demonstrate this principle through a series of experi-
ments that are presented in Section 5. In Section 6,
we present the DH LWIR setup for monitoring defor-
mation of large reflectors and the results obtained in
the laboratory. Section 7 presents the implementa-
tion of the setup in the cryogenic vacuum facility
at the CSL and verification of the method during
2. Holography with CO2Lasers: A Review
recording at 10.6 μm and readout in the visible with
an He–Ne laser . Many works followed by other
groups that used a similar setup and recording med-
wax and gelatin films , bismuth thin films
[32,35,36], acrylic and thin films , wax [38,39], oil
films deposited on glass plates , resists , poly
(acrylic acid) films [42,43], and albumen . All
these materials are able to record patterns through
relief variations, producing phase holograms that
can be processed in situ. Also they show relatively
good figures of merit in term of diffraction efficiency.
But what seems to remain limited is the resolution of
such media with a rapid drop of diffraction efficiency
for line spacings larger than 10 lines per millimeter.
Also, they all use visible wavelengths for readout,
which does not make the application of these materi-
als for real-time HI easy. Double-exposure holograms
that are readout with visible lasers have also been
Analog Recording of Holograms with CO2Lasers
The very first evidence of LWIR holographic electro-
nic recording was provided by Løkberg and Kwon
, who demonstrated electronic speckle pattern in-
terferometry (ESPI) with CO2lasers and pyroelectric
vidicon cameras. ESPI consists in recording the in-
terference of object wave Uo?x;y? and a reference
wave UR?x;y? at the level of a camera focal plane.
In ESPI this interference is called a specklegram,
and the optical imaging system has its aperture
small enough to generate speckles in the object
Electronic Recording of Holograms with CO2Lasers
wavefront. Also, to obtain a specklegram that can
be resolved by the array sensor, the object and refer-
ence wavefronts need to match as closely as possible
to each, and in-line reference beams (RBs) are used
. Specklegrams recorded at different instants are
subtracted from each other to obtain fringe patterns
that can be related to the object deformation under-
gone between these instants.
Applying ESPI with pyroelectric cameras is not
easy since the latter are sensitive only to changes
in the radiation energy. Therefore, Løkberg and
Kwon worked exclusively with vibrating objects for
which the speckle pattern intensity was intrinsically
The second evidence of electronic recording of ho-
lograms in the LWIR was made by an Italian group
who showed for the first time to our knowledge the
use of DH at 10.6 μm . DH is a more modern
approach of holography, which consists of recording
holograms directly on an imaging array sensor. In
DH the intensity pattern (hologram) IH?ξ;η? recorded
in the plane of the array sensor ?ξ;η? is used to recon-
struct numerically the complex object wave field
Uo?x;y? located in the plane ?x;y? situated at a dis-
tance d from the hologram plane/sensor. If the refer-
ence complex amplitude in the hologram plane is
given by R?ξ;η?, the object field is given by the
Fresnel transform [23,46]:
In practice, the hologram is sampled by the array
sensor on M × N pixels, of dimensions Δξ × Δη.
Therefore, Eq. (1) can be written in a discrete form,
yielding the computation of the object on M × N
points, say Uo?m;n?, with m ? 0;1;…;M − 1 and
n ? 0;1;…;N − 1. Noting the similarities between
Fourier transform (FT) and Eq. (1), the computation
of this field consists in applying an inverse discrete
FT to the product of the three first factors under the
integral of Eq. (1), say
λd?xξ ? yη?
The authors in  point out that the terms out-
side the sum only affect the overall phase of the
A104APPLIED OPTICS / Vol. 52, No. 1 / 1 January 2013
object field. In a typical HI application, where we are
only interested in the object deformation, these
terms remain constant, and they can be neglected
in the computation.
The deformation (or displacement field) is related
to the phase difference between two states of the
object. The phase of the object wave in every point
of the object plane is given by
φ?m;n? ? tan−1
In digital HI (DHI), one computes the phases for two
consecutive states φ1and φ2of the object and sub-
tracts one from the other to deduce the displacement.
An advantage of DH over ESPI is that it allows the
phase to be retrieved from a single acquisition. An-
other advantage of DH is that the setup does not
necessitate an imaging lens in front of the sensor
(like in ESPI) because the image of the object is re-
constructed numerically and correct focusing of the
image is obtained by setting the distance d in Eq. (2)
at the same value as the one used experimentally.
DH in the LWIR was first demonstrated by
Allaria et al. . They recorded holograms in Mach–
Zehnder optical configuration with pyroelectric array
sensors  for reconstructing transmission objects.
More recently the same group showed further results
in measuring the three-dimensional (3D) shape of re-
flective objects, again with the same Mach–Zehnder
configuration  and pyroelectric camera.
Other LWIR array sensor technologies offer advan-
tages over pyroelectric cameras, in particular un-
cooled microbolometer arrays . Recently George
et al. showed DH based on a microbolometer array
 with an optical setup similar to that of  and
. Microbolometers are now an emerging technol-
ogy with a growing market and apply to thermogra-
phy in many civilian, military, and industrial sectors
[47,51]. Recently manufacturers have shown mega-
pixel formats , which make them really attractive
for developments of DH at such wavelengths.
Microbolometer arrays with medium resolutions
(320 × 240 pixels) were considered in ESPI with CO2
lasers in our early experiments with in-plane ESPI
 and later with out-of-plane ESPI and lensless
off-axis DHI  with the purpose of measuring large
specular objects. We recently showed nondestructive
testing of larger objects with a 640 × 480 pixel micro-
bolometer camera (Variocam hr from Jenoptik)
[54,55]. With the purpose of display of increasingly
larger objects, the Italian group also considered
medium pyroelectric array to larger microbolometer
array formats (640 × 480) under several configura-
Both groups note the interest of using such long
wavelengths in DH [53,56–58] for reconstructing
large objects when compared with similar setup in
the visible: the maximum admissible angle between
the reference and object beams is given by
θmax? 2 arcsin
for square pixels with dimensions Δ ? Δξ ? Δη. The
angle θmaxsets the observable size of the object if the
?1 diffracted orders needs to be clearly separated
from other terms. When analyzing the ratio λ=Δ
for visible and CO2wavelengths and current sensors
in both domains, one easily determines that θmaxis
from 5 to 10 times larger in the LWIR than in the
3.Particular Aspects of LWIR for DH
The microbolometer arrays that are used in conjunc-
tion with CO2lasers in our experiments have a spec-
tral sensitivity ranging from 8 to 14 μm. As is known
in fundamental physics, black bodies at a given tem-
perature emit radiation in a certain wavelength
range (Planck’s law) and Wien’s law states that
the product of wavelength of maximum spectral
radiance and the temperature is a constant equal
to 2.8977 × 106nm:K.
It can be calculated that the wavelength of CO2la-
sers corresponds to ambient temperatures around
20°C. Radiation emitted by anything in the environ-
ment of work could reach the sensor directly or by
reflection on either the object itself or some parts
of the setup. It is then important to understand
the effect of such thermal backgrounds in DH. Let
us first note that this background is incoherent.
Therefore, it does not participate in the building of
the hologram and then cannot be propagated by
DH. Nevertheless, it will appear as an additive noise
component in the intensity of hologram IH?ξ;η?. We
have analyzed what a typical contribution of thermal
background could be in DH. We consider a lensless
DH setup [like what will be presented in Section 5
(e.g., Fig. 6)] but without either an object in the field
or a laser beam switched on. Then the camera
catches some radiation from the environment of the
setup, as is shown in Fig. 1(a). We call the thermal
contribution IThermal?ξ;η? in the plane of the sensor.
When injecting this image in Eq. (2), in place of
the product IH?ξ;η?R?ξ;η?, and using a typical recon-
struction distance d of 1 m, we obtained a central
peak shown in Fig. 1(b). The extent of this peak will
strongly depend on the presence of any object acting
LWIR lensless DH setup and (b) contribution to the numerical
(Color online) (a) Typical thermal background in an
1 January 2013 / Vol. 52, No. 1 / APPLIED OPTICSA105
as heat source in the field of view, and therefore we
cannot draw any generality from the example shown.
Therefore, we propose to filter this noise in the
same way as other authors remove noise in DH. In
all experiments presented in this paper, we apply
DC-term filtering  as well subtraction of refer-
ence (R) and object (O) components from the holo-
gram (H), called HRO subtraction, introduced by
Skotheim for removing the halo term .
The HRO subtraction consists of using modified
hologram intensity I0
Eq. (2) and from which images of reference and object
beams, IR?ξ;η? and IO?ξ;η?, respectively, are deduced.
These images are captured independently by using
shutters in both beams, prior to hologram capture.
Here we will use the same approach but subtract also
the thermal background (T) in addition to the refer-
ence and object components from the hologram H,
what we will call “HROT subtraction.” The intensity
of the hologram to be injected in the numerical recon-
struction is then given by [leaving aside the ?ξ;η?
H?ξ;η? in place of IH?ξ;η? in
H? IH− IR− IO− ITherm:
We must also take into account that the images of
reference and object beams contain the same thermal
background. Assuming that the latter has not chan-
ged between acquisitions, we can deduce it from the
measurements of both other beams. If we add the suf-
fix m to designate the measured images, we can write
the hologram intensity to be used in the reconstruc-
tion as follows:
? IH;m−IR;m−IO;m?ITherm;m: (6)
The relationship between the observed surfaces
roughness and the illumination wavelength shall
be considered with importance if one wishes to know
with which kind of reflectivity one deals prior to
developing an optical instrument. In the case of
holography/speckle methods, generally having pure
(diffuse) scattering reflectivity is preferred because
therefore classical imaging systems can be used to
focus on the object. In DH, the same is true, and a
pure scattering surface will allow numerical focusing
without difficulty. Working at longer wavelengths
than visible will strongly impact the reflectivity type,
as was already mentioned by authors working in
LWIR . Yamaguchi  has shown that, when the
wavelength is close to the surface roughness or smal-
ler, the surface becomes completely scattering and
speckle appears. On the other side, specular reflec-
tion appears as soon as the wavelength is larger than
the roughness and quickly dominates the speckle
pattern intensity. Nevertheless, up to some extent
Relationship between Surface Roughness and
the speckle pattern still can be observed, but its in-
tensity is smaller than the specular peak. The total
integrated scatter (TIS) represents the scattered
light intensity normalized by the intensity of the re-
flected beam. It is proportional to the square of the
ratio between the roughness and the wavelength
. Consequently, if the wavelength is 20 times lar-
ger, the TIS will be 400 times smaller. Thus, the
speckle intensity will be 400 times smaller using a
CO2laser than with an equivalent experiment using
a visible laser. In the visible, this problem is well
known, and holography/ESPI observation of surfaces
having a strong specular reflection requires spraying
surfaces under test with scattering powder.
We already discussed this in our earlier works ,
and for metallic surfaces with roughness in the range
of a few nanometers, we dealt with this problem by
spraying the surface with a white removable powder
(developer for liquid dye penetrant nondestructive
technique), which is largely used by holographers.
In the frame of more recent works related to ESPI
with CO2lasers for nondestructive testing on aero-
nautical composite structures, we measured the
roughness of various materials of interest for that
application and found that they were of the same
order as the wavelength . This allowed producing
speckles in LWIR without spraying the surface, and
we were able to apply DHI for successful measure-
ment of large deformations and detection of defects
in such samples [54,55].
In the intermediary cases where both specular and
scattering reflectivities are observed, one has to be
highly cautious to avoid specular peaks that could sa-
turate or overload the microbolometer array, either
by tilting the object (hence placing the specular peak
out of the field of view of the sensor) or by spraying
the surface with a diffuse scattering material .
The request for our project is that the LWIR DH tech-
nique has to be adapted to aspheric reflectors, which
can be either astigmatic (such as parabolas) or stig-
matic (such as ellipses), with slopes that can be quite
high as well as showing asymmetric slope changes
(like in the case of free-form RF reflectors). Another
constraint is that these reflectors can be purely spec-
ular or partially specular and scattering, as a func-
tion of their roughness and the test wavelength
used. It must be noted that, most of time, these re-
flectors have roughness very small compared to the
wavelength, yielding specular reflection.
Having this in mind, two basic cases have been dis-
in the case of a parabolic reflector but can be ex-
tended to other shapes. The first one considers the
reflector in pure specular illumination and observa-
tion configurations [Fig. 2(a)]. The second one consid-
ers intermediary diffusers, either at the illumination
stage [Fig. 2(b)] or at the observation [Fig. 2(c)]. In
the figure, the illumination and observation are
not coaligned, but this is for sake of simplicity.
Choice of the Most Appropriate DH Configuration
A106 APPLIED OPTICS / Vol. 52, No. 1 / 1 January 2013
The pure specular case shown in Fig. 2(a) is in fact
similar to classical interferometer (of the Mach–
Zehnder type) and makes use of illumination
through a spherical lens with the point source at ty-
pically two times the parabola focal length. In this
case rays do not converge in a single point, and a col-
lecting lens (CL) is necessary to intercept the exter-
nal rays prior to make them interfere with the RB
through the beam combiner (BC). The diameter of
CL has to be adapted to the optics under test without
being necessarily matching perfectly the object wave-
front, aswould be the case with dedicatednull lenses.
This non-perfect-matching between the object and
RB is not a problem for DH since the technique
allows the reconstruction of different parts of the
object by adapting the distance d in the numerical
The second case, presented in Fig. 2(b), makes
use of diffuse illumination produced by enlarging
the object beam (here with a negative lens), which
illuminates a transparent ground glass diffuser, gen-
erating a speckled wavefront, which is then reflected
by the specimen. This principle has been already
demonstrated in HI and ESPI for testing specular
objects in visible wavelengths [64–66] and also in the
case of transparent objects (for fluid convection ana-
lysis) . The scattered light reaches the mirror,
which reflects all rays specularly. Part of these rays
reaches the camera through the imaging system.
These authors note that the imaging system should
be focused on the specular object to achieve maxi-
mum of contrast in the fringes . Here the CL
can be either an imaging lens or any lens to ease col-
lection but not necessarily imaging the object.
Alternatively, no collection lens could be used. In
any case, the DH reconstruction algorithm has to
be adapted to the situation.
In the third case, the illumination is similar to
the pure specular case in Fig. 2(a) but the rays are
directed on a diffuser which acts as an intermediary
scattering object for DH. We already have used such
approach with HI using photorefractive crystals
[17,18] at 532 nm for measurements of smaller
We have analyzed the different scenarios and
made a trade-off between the pure specular and the
scattering cases. In the specular case, we computed
by ray tracing the spot sizes that are obtained with
typical parabolic reflectors of interest, taking into ac-
count realistic figures of slopes provided by the ESA.
It appears that, apart from some examples, the spot
size is often too large for the state-of-the-art detec-
tors when no CL is used. In other cases, lenses
needed to be built to either illuminate and/or collect
light in the case of very large aperture (e.g., for ellip-
tic reflectors). Despite this limitation, the specular
case is expected to provide the best interference qual-
ity (like in classical interferometry) since it is not dis-
turbed by speckle.
As mentioned above, similar setups of HI and
ESPI have been demonstrated at visible wave-
lengths, making use of ground glass transmission dif-
fusers. Nevertheless, transmission diffusers made of
infrared transparent material (ZnSe, Ge) for working
with CO2lasers were not found on the market and
had to be custom made. Therefore, we envisaged
using roughened metal plate reflecting diffusers.
On that basis we kept the principle depicted in
Fig. 2. Potential schemes for DH setup for large specular reflector.
1 January 2013 / Vol. 52, No. 1 / APPLIED OPTICSA107
Fig. 2(b) and not Fig. 2(c). Indeed the design of the
setup appeared easier with a diffuser replacing a
folding mirror in the illumination arm than in the
observation, specifically in view of incorporation in
our vacuum facility.
Although we did not suspect any counterindication
to apply such schemes to DH in LWIR, we have
performed simple experiments for checking the va-
lidity of using diffuse illumination in DH, prior to full
scale implementation. This is presented in detail in
A simple experiment for demonstrating the possibi-
lity of using diffuse illumination with DH has first
been set up in visible light as shown in Fig. 3. A
diode-pumped solid-state laser at 532 nm is first
expanded, and part of the collimated beam (RB) is
reflected by a beam splitter (BS) and directly travels
to a CCD camera after reflection by a BC. Another
part of the laser beam is transmitted by BS and is
further expanded and folded to reach a reflective dif-
fuser D. The latter consists of a metallic plate rough-
ened by sanding. Although we have not measured its
roughness, we can say that it reflects partially spec-
ularly and diffusively. The setup configuration is a
lensless Fresnel DH setup with off-axis RB. The size
of the object has been limited, and the angle between
reference and object beams has been chosen for
having good separation of the different terms at
the reconstruction. Fig. 4 shows the result of the nu-
merical reconstruction [Fig. 4(a)], the masked image
of the focused object selected [Fig. 4(b)], and a zoom of
the speckle pattern located in the plane of the mirror
object [Fig. 4(c)]. It can be seen that the average in-
tensity ofthe speckle image is not homogeneous. This
is because the surface of the diffuser was partially
specular and a perfect Lambertian scattering profile
Diffuse Illumination in DH for Specular Objects
proved difficult to obtain by means of a sanding
We have analyzed the behavior of the speckle pat-
tern when the mirror object is rotated and for differ-
ent distance of DH reconstruction. Fig. 5 shows the
zoomed speckles in two situations. The first one
[Fig. 5(a)] concerns the case of correct numerical
focusing; i.e., the hologram is reconstructed with
distance d equal to the true distance between the
specular object and the sensor plane. The second one
[Fig. 5(b)] concerns out-of-focus reconstruction. Each
shows speckle grains of which positions are com-
pared before and after rotation, left and right images,
respectively. In the case of correct numerical focus-
ing, when the mirror object is rotated out of plane,
no speckle movement appears. The only variations
are intensity changes of speckle grains. On the con-
trary, in the case of incorrect numerical focusing,
speckle movement is observed during object rotation.
This should cause decorrelation degrading the fringe
visibility, as was observed by Hansen with HI and
ESPI using an imaging lens [65,66].
On the basis of this first experiment in the visible,
we settled a similar setup with a CO2laser and a mi-
crobolometer array camera to perform displacement
field metrology on a specular surface (Fig. 6). The
beam from the CO2laser (from the VM-TIM com-
pany, emitting 8 W at 10.6 μm) is split in two parts
by a BS that reflects 90% of the beam and transmits
10% (ratio R90=T10). The transmitted part is the RB
that is folded, expanded, collimated, and then direc-
ted onto the microbolometer camera through the BC.
The latter is a Jenoptik Variocam hr camera module
(640 × 480 pixels, pixel size Δ ? 25 μm) without ob-
jective lens attached. The BC is a R50=T50 BS. Both
BS and BC are BSs made of ZnSe glass with suitable
coating. The beam reflected by BS is expanded and
folded to illuminate the diffuser. The latter is made
Fig. 3.Setup at 532 nm for studying DH on specular object illuminated by a reflective diffuser.
(a) Numerical reconstruction of the hologram, (b) masked object at focused position, and (c) zoom of speckle located on the specular
A108 APPLIED OPTICS / Vol. 52, No. 1 / 1 January 2013
of a metallic plate (Invar) that is coated by a scatter-
ing powder yielding generation of speckle that can be
resolved after reflection onto the specular object. The
object is a plane mirror (80 mm diameter) coated
with aluminum mounted on a rotation stage for per-
forming well-controlled out-of-plane rotation (tilt).
Since the laser is polarized, the setup also includes
a polarizer P that allows the reduction of the RB
power and then equalizing reference and object beam
intensities at the level of the array sensor for maxi-
mizing the hologram contrast. The angle between
both beams has been arranged to allow off-axis
DH and clear separation of diffracted orders.
Fig. 7(a) shows the result of DH reconstruction in
amplitude, and Fig. 7(b) the same after applying
filtering of DC term  and HROT subtraction
explained in Section 3.A. To apply the HROT sub-
traction, one must record separately the thermal
background and object and RBs independently to
one another during a preliminary step, which is
possible by adding shutters placed in the object
and reference arms, Sh1 and Sh2 in Fig. 6, respec-
tively. Figure 7(c) shows the difference of the recon-
structed phases obtained after rotation of the mirror.
Figure 7(d) shows the useful part of the mirror from
which we deduced the displacement, knowing the
geometry the rotation angle.
To perform analysis of the metrological perfor-
mances of the technique, we have used a commercial
interferometer from HP (model 5519A) for simulta-
neous high-accuracy measurement of the rotation
angle by attaching necessary retroreflecting ele-
ments to the rotation stage of the test reflector. We
varied the angle and captured the hologram and sub-
sequently performed computation of the angle from
the recovered phase differences. The angles obtained
by DHI are plotted, in Fig. 8, as a function of those
measured directly by the HP interferometer, as is
shown. These measurements show a good agreement
except for higher angles where the fringes cannot be
resolved anymore. The measurement uncertainty of
the commercial interferometer is 0.1 arc sec and cor-
responds to a displacement of 0.036 μm for the tested
mirror. Therefore, one can consider that the differ-
ence between the measurement performed by the
DH with diffuse illumination and the commercial in-
terferometer corresponds to the uncertainty of the
DH method. These results allowed us to determine
that the uncertainty of DH is 1.5 μm as long as
the number of pixels per fringes is higher than 13.
It must be noted that, if the diffuse illumination
works well with small plane objects, it can become
more difficult to apply with large mirrors, especially
ular object rotated out of plane: (a) DH reconstruction correctly
focused on specular object and (b) DH not correctly focused.
Observation of speckle (zoomed image) reflected by a spec-
illuminated by a reflective diffuser.
Setup for studying DH in LWIR on specular object
(c) phase difference after rotation of mirror, (d) excerpt of phase difference on the mirror zone.
Numerical reconstruction of a plane mirror by DH in the LWIR: (a) amplitude, (b) amplitude after filtering of DC term and HROT,
1 January 2013 / Vol. 52, No. 1 / APPLIED OPTICSA109
convex ones, or with specular surfaces with arbitrary
shapes. In the cases of interest in our applications,
we most often have to test concave mirrors, which
are probably the easiest ones to deal with, even with
very large reflector sizes.
The test specimen that is used in the experiment is a
demonstration reflector of the ESA space mission
HERSCHEL . Technological demonstrators of
submillimeter reflectors were developed during early
studies of the mission (earlier named FIRST, for Far
InfraRed and Submillimetre Telescope), and one
of them is considered for demonstration of our tech-
nique, as was also the case in previous developments
[ 17,18]. The test object (Fig. 9) is a concave parabola
made of a carbon fiber reinforced plastic structure
with gold coating. It has a diameter of 1.1 m and focal
length f ? 1.58 m.
As already discussed, we selected a scheme corre-
sponding to Fig, 2(b), with diffuse illumination
provided by a reflective scattering plate. To limit
aberrations, it is preferable to work with illumina-
tion and observation in line. Therefore, the design
is based on a Mach–Zehnder configuration and is
shown in Fig. 10. The elements of the drawings
are at the same scale except the reflector, of which
size and distance to the setup are reduced, as well
as the least confusion circle (LCC), which is drawn
larger that actual size. The laser beam is expanded
by combination of lenses L1–L2. The beam is split in
two by the beam splitter BS1 (R1=T99). The trans-
mitted part is expanded by lens L3 and illuminates
the reflective diffuser D. The latter is an Invar plate
that is covered by white scattering powder already
discussed in Section 5 and that has a roughness of
DH Setup for Observation of Aspheric Reflectors
typically 4 μm. This makes the diffuser partially
specular and scattering. It is placed at 45° incidence,
which folds the beam toward beam splitter BS2
(R50=T50), which in turn illuminates the reflector.
The diffuser is placed at around 2f, i.e., 3.16 m, and
the parabola reflects the beam backward in the direc-
tion of BS2. The rays are focused in a blur spot (LCC).
A ray tracing allowed location of the LCC near 2f, at
3.194 m from the reflector. This spot could be located
directly at the sensor S position and superposed to
the RB. However, as is shown in the figure, we placed
a relay system formed by combination of lenses L4
and L5. Therefore, the LCC is imaged on the array
sensor of the camera. The reason for this addition
is twofold. First, it allows resampling of the object
image to adapt its size to the detector by adjusting
the focal length ratio between L4 and L5. Second, it
is related to the implementation of this setup in a va-
cuum chamber, which we will present in Section 7.
Because both the laser and the LWIR camera are
not vacuum compatible, they have to stay out of the
chamber and beams have to pass through LWIR win-
dows of which thickness must be adequate to avoid
bending and failure due to the pressure difference.
In function of these constraints and other ones re-
lated to the geometry of the vacuum chamber access
flange, the only position for these windows is as
shown by the dotted line in Fig. 10. One window will
be placed in the enlarged collimated beam between
L2 and BS1, and a second one between L4 and L5.
The RB is formed by the part of the beam reflected
by BS1. It is first made incident to a mirror mounted
on a piezo translator (MPZT), which reflects it back-
ward through BS1 and the BC (R50=T50), which in
turn reflects it partly onto the sensor. A lens L6 is
placed in the collimated RB and forms an afocal
0 20 40 6080 100120140 160 180 200
HP interferometer measurements (arcsec)
Digital holography measurements (arcsec)
rotationanglefromLWIR DHIofamirrorilluminated byreflective
diffuser and those measured directly on the same mirror using a
(Color online) Comparison between the measurements of
(Color online) FIRST demonstration reflector on its
A110APPLIED OPTICS / Vol. 52, No. 1 / 1 January 2013
system with lens L5 in such a way the RB is colli-
mated on the sensor. The RB can be made incident
at an adequate angle on the sensor for applying
off-axis DH. Avariable neutraldensity filter isplaced
in the reference arm for equalizing the intensities of
object and RBs on the sensor. Two beam dumps are
placed in transmitted beams which are not used in
the setup. At last two shutters (Sh1 and Sh2) are
used for separate acquisition of object and reference
images for filtering noise in the image, as discussed
earlier in the paper.
It is possible to calculate analytically the maxi-
mum size of the object from the sampling require-
ments as well as the geometry of the object and RB.
For that, we followed an approach similar to 
where the authors considered the case of in-line
Fresnel DH. Here we apply it to off-axis DH. First,
let us consider that the sensor with pair L4–L5 in
front is equivalent to a lensless system because it
only acts as relay imagery from the LCC to the sensor
(with possible magnification). Therefore, we have a
recording situation depicted in Fig. 11 where the
object is the LCC and rays from the object interact
with the RB, which is collimated and is oriented to
avoid overlapping of reconstructed orders. We can
determine the largest angle θ between the object
and RBs. As is shown in Fig. 11, this angle is formed
by the ray issued from the lowest point of the LCC
and reaching the highest point of the sensor S, on
the one side, and the lowest ray of the RB on the
other side. The maximum value of this angle θmax
is deduced from the sampling theorem and given
by Eq. (4), which can be simplified in the case of small
angles to θmax? λ=2Δ. The pixel dimension of the
Variocam is Δ ? 25 μm, which gives a maximum
angle of 0.212 rad. From Fig. 11, it comes that the
size of the object is related to this angle by
L ? NΔ
from which we find that the maximum size of the
Lmax?λd − 2NΔ2
Since L4 and L5 can have different focal lengths, f4
and f5, respectively, they can be used for optimizing
the sampling of the object image to benefit as much
as possible of the sensor resolution. If we define
Δ0? ?f4=f5?Δ, the size of the object L0maxis now
inthe planeLCC by
with d0the distance between LCC and the reflector of
which value was found by ray tracing to be equal to
3.194 m. With equal focal lengths for L4 and L5
N ? 480,
L0max? 0.665 m. This value is smaller than the ac-
tual size of the reflector, which is 1.1 m. Therefore,
we will have an overlap of the reconstructed orders.
For avoiding this, we can use different focal lengths
it is found that
Fig. 10.Final design of the LWIR DH interferometer with diffuse illumination for large space reflector.
Fig. 11. Geometry of the DH recording setup.
1 January 2013 / Vol. 52, No. 1 / APPLIED OPTICSA111
for the pair L4–L5. We found stock ZnSe lenses with
f4? 75 mm and f5? 127 mm, which gives L0max?
1.139 m and is compatible with the reflector.
Although the image and its conjugate are well
separated under these conditions, the resolution of
the useful image is not maximized because it occu-
pies one quadrant of the detector, i.e., maximum
240 × 240 pixels, which is poor. To maximize the spa-
tial resolution, we have another possibility, which is
to allow overlapping orders and using the phase
shifting to separate orders , which is typical to
the in-line DH configuration. The phase-shifting
technique has been implemented in the setup by
means of the MPZT (in Fig. 10). Several images
are recorded in sequence between which the mirror
is shifted perpendicularly to the beam to create a pis-
ton effect between the images. This technique has
the disadvantage that it takes a longer time for cap-
ture compared to the single-shot capability of off-axis
DH. Moreover, it further imposes some stability in
the setup during the acquisition sequence. Therefore,
we lose the interest of off-axis DH and its possibility
to access the phase of high-speed phenomena in
single shot. Nevertheless, in the case of cryogenic
tests, as presented in the Section 7, the temperature
changes are quite slow and the acquisition times can
be considered extremely small in comparison. From
equations similar to Eq. (9) but dedicated to the
in-line case , we calculate that, with f4? f5,
we obtain L0max? 1.34 m. Figure 12 shows the re-
sults obtained after application of this technique to
reconstruct the parabolic reflector, both in modulus
[Fig. 12(a)] and in phase difference [Fig. 12(b)] after
an out-of-plane rotation is applied to the reflector. It
must be noted that the object is not on the same op-
tical bench than the DH setup. Despite this, we were
able to capture holograms without difficulty and with
perturbations in the laboratory (vibration and equip-
ment noise, people circulating, etc.), whereas this
was not possible with interferometers in the visible.
Following the laboratory validation, the interferom-
eter has been implemented in the FOCAL5 vacuum
chamber of the CSL  to measure the deformation
of the reflector at cryogenic temperatures. The facil-
ities of the CSL are all equipped with optical benches
that are standing on a seismic block disconnected
Application in Cryogenic Test
from the building and the vacuum chamber itself.
The throughputs of the feet of the optical bench
are especially designed to not allow for leakage when
the vacuum is made into the chamber. Such optical
benches are a prerequisite for interferometric moni-
toring of large specimens because they damp any
vibration coming from the building or outside. The
chamber has a 5 m diameter and is 10 m long. It
is fully equipped with nitrogen and helium circula-
tion circuits with regulation for reaching specific
temperature sequences on specimens.
The configuration of the thermal-vacuum test uses
the same optical configuration as in Fig. 10. However,
the opticalsetuphasbeensplitin twoparts, asshown
in Fig. 13. The first part is outside the vacuum cham-
ber (outer bench) and holds the vacuum-incompatible
equipment (i.e., the laser and the thermographic
camera). The second part (inner bench) is inside
the chamber and contains the interferometer. The se-
paration and combination of the object beam and RB
is realized in the chamber to minimize the impact of
differential vibration between the inner and outer
bench. The dimensions of the optical setup (inner
and outer benches) are exaggerated with respect to
the facility and reflector dimensions. Also, the DH
setup is drawn vertically, whereas it is actually hor-
izontal. The reflector is located at the adequate dis-
tance from the interferometer and surrounded by a
thermal shroud. The latter is made of copper plates
painted in black on their inner part and connected to
nitrogen circulation pipes. The shroud allows chan-
ging the temperature on the reflector through radia-
tive transfer, and it is completely closed except for a
small aperture for the beams to reach the reflector
and be reflected backward to the DH setup.
Several thermal cycles were operated and the ho-
lograms were captured on a regular basis. Numerical
reconstruction was performed, and the phase differ-
ence was computed between pairs of temperature
states during the cycle.
The measurement of the displacement field for a
temperature variation from 224 K (where the initial
digital hologram is recorded) down to 107.5 K of the
reflector is shown in Fig. 14: Fig. 14(a) is the raw
phase difference, Fig. 14(b) is the masked region of
interest obtained after applying a median filtering
on Fig. 14(a), and Fig. 14(c) is the unwrapped phase
 from which the displacement field can be deduced
. Figure 14(d) shows the total displacement field,
and Fig. 14(d) (Media1) showsthe displacementevol-
ving in function of temperature. We are interested
in the deformation that is obtained by removing the
rigid body motions from the total displacement field.
These are tilts and defocus that were removed from
the phase by Zernike analysis . The remaining
result is shown in Fig. 15(b).
For validating the performance of the LWIR DH
interferometer, the results have been compared to
measurements made on the same reflector some
years before, with a high spatial resolution LWIR
interferometer also developed at CSL  and which
with diffuse illumination. (a) Modulus and (b) phase difference
after out-of-plane rotation of the reflector.
Application of phase-shifting DH to the FIRST reflector
A112 APPLIED OPTICS / Vol. 52, No. 1 / 1 January 2013
made use of a null lens. We compare the deformation
measured with the two techniques in Fig. 15 for the
same temperature range. The RMS difference is
1.6 μm, which is close to the measurement uncer-
tainty that we found for the DH technique with
diffuse illumination (Section 5).
Fig. 13.(Color online) Scheme of the DH interferometer implemented in the vacuum chamber FOCAL5 of the CSL.
(c) after phase unwrapping, (d) 3D plot of total displacement (Media 1 shows increasing displacement when temperature changes).
(Color online) Displacement field obtained between 224 and 107.5 K. (a) Phase difference, (b) after masking and median filtering,
1 January 2013 / Vol. 52, No. 1 / APPLIED OPTICSA113
We have presented the development of a digital holo-
graphic interferometer in the LWIR and which uses a
CO2laser and a microbolometer array sensor. The
target application is the cryogenic test of large space
aspheric reflectors working in the far-infrared and
The advantage of an LWIR digital holographic in-
terferometer is twofold: first, it is able to measure
deformations 20 times larger than similar inter-
ferometers working in the visible, and second, the
stability constraint of the holographic setup is re-
laxed. The second advantage of LWIR DH is that is
can reconstruct objects 5–10 times larger than in the
visible. We have discussed some features related to
the LWIR. First, an incoherent thermal background
is present in the hologram, and we proposed a simple
way to filter it. Second, the reflectivity appears more
specular in the LWIR than in the visible. This dif-
ficulty coupled to the fact that the aspheric space
reflectors are intrinsically specular led us to study
the possibility of diffuse illumination. Starting from
similar experiments in visible ESPI, we show that a
reflective diffuse illumination can be used for illumi-
nating specular objects that are further recon-
structed numerically by DH. We first have proven
this in the visible and then in the LWIR spectrum,
prior to applying it to the measurement of the rota-
tion of plane mirrors.
Then we presented in details the design of our
LWIR DH interferometer, which makes use of diffuse
illumination and which is used for observation of a
parabolic reflector [coming from the ESA FIRST
(HERSCHEL) project]. We have shown that, among
the different existing DH geometries, the in-line con-
figuration with phase shifting is the most appropri-
ate in terms of resolution for our object. The fact that
phase shifting implies a longer time of image capture
is not a problem because the deformations that will
Conclusions: Future Prospects
be observed during cryogenic tests are much slower
than the phase-shifting sequence.
After development of the DH setup and verifica-
tion on the FIRST reflector in the laboratory, the
whole setup and specimen was implemented in a
cryogenic facility of the CSL, where vacuum-thermal
cycling was operated and the deformation measured
during this time. The results are found in very good
agreement with similar tests performed with classi-
cal LWIR interferometry making use of null lens.
We point out here that, compared to classical null-
lens interferometry, DHI allows a much simpler
approach and that components of the shelf can be
used. Indeed, DH can reconstruct image of object
at arbitrary distances, and there is a priori no need
of closely matching the aspheric wavefront with an
expensive and dedicated optical assembly like a null
lens. The diffuse illumination helps in the fact that
it generates rays that can be collected easily by
simple lenses and that form an object beam that
can interfere with a RB in a DH setup. This simple
principle opens the way for testing more complex
specular reflectors, either aspheric (astigmatic or
stigmatic like ellipses) or arbitrary shapes like free-
form RF reflectors used for Earth telecommunica-
tions from space.
At the time of writing this paper, new experi-
ments are ongoing for comparing the diffuse illumi-
nation with the specular case, as is discussed in
Section 4. Also the case of an elliptic reflector (such
as secondary reflector of the Planck telescope) will
be treated as well. We also investigate the pos-
sibility of testing free-form telecommunication an-
tenna reflectors, which is an even more challenging
The developments presented in this paper have
been realized in the frame of the ESA General Sup-
port Technology Programme (GSTP) project, contract
removal of tilt and defocus showing comparable and reproducible deformations.
(Color online) Comparison between previous results obtained (a) by LWIR interferometer with null lens and (b) DHI, both after
A114 APPLIED OPTICS / Vol. 52, No. 1 / 1 January 2013
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